Moving the Goalposts is the practice of arbitrarily moving the criteria for "proof" or acceptance out of range of whatever evidence currently exists.

Examples:
Apologist: Evolution must be false because life forms obviously don't change.
Counter-Apologist: Breeders have developed hundreds of unique breeds in just the past 300 years.
A: Well, that's just microevolution. You can't create a new species.
C: Ever try to cross a Chihuahua with a Great Dane?
A: Ok, but you just get a new species of the same kind. You can't create a new kind.

It should be noted that changing criteria is a fundamental part of science. Science must be able to reject earlier, less precise theories in order to adopt more accurate worldviews. An example is Newtonian physics, which becomes an inaccurate predictor of events when applied to very small objects (like electrons) or to objects moving at relativistic speeds.

The difference between legitimate modification and Moving the Goalposts is the arbitrary nature of the latter.